Outline “Search for octupole-deformed nuclei for enhancement of atomic EDM” 1Umesh Silwal, 2Prajwal Mohanmurthy, 1Durga P. Siwakoti, 1Jeff A. Winger 1Mississippi State University 2LNS, Massachusetts Institute of Technology June 06, 2019 MENU-2019 Cohen University Center, CMU June 02-07 Pittsburgh, PA

Outline MENU-2019 Introduction: why is EDM important? Attempts to measure the EDM General technique of measuring EDM Need of Octupole deformed nuclei EDM enhancement Survey results, and Future Research MENU-2019 October 25-28, 2017 Pittsburgh, PA Cohen University Center, CMU June 02-07 Pittsburgh, PA

- + Introduction 𝑑 =𝑞 𝑙 l What is EDM? Any two point charges with equal magnitude but opposite signs separated by small distance is called electric dipole. Source of EDM is mainly,  in CKM matrix, and QCD-θs . But CPT-Violation, SUSY all can cause and may also enhance the SM-EDM.  Source of EDM? 225Ra Fig: source google

Introduction Why EDM is Interesting? P-violation: τ-θ puzzle Parity is conserved in electro-magnetic and strong interactions but must not conserved in weak interaction. 𝑃 𝐿𝐻𝑆 =−1) 𝜅 + ( 𝜏 + )= 𝜋 + + 𝜋 + + 𝜋 − ( 𝑃 𝑅𝐻𝑆 =−1 𝑃 𝐿𝐻𝑆 =−1) 𝜅 + ( 𝜃 + )= 𝜋 + + 𝜋 0 ( 𝑃 𝑅𝐻𝑆 =+1 Wu et al., in 1957 observed that β-decay of 60Co preferentially emitted against the direction of the spin of it which tells that weak interactions violates parity maximally. CP-violation: Natural kaon decay CP is marginally violated as neutral kaons oscillated to their anti-particles. 𝐶 𝑃 𝐿𝐻𝑆 =1) 𝜅 1 → 𝜋 + + 𝜋 − (𝐶 𝑃 𝑅𝐻𝑆 =1) ( 𝜏 1 =8.95× 10 −11 𝑠 𝐶 𝑃 𝐿𝐻𝑆 =−1) 𝜅 2 → 𝜋 + + 𝜋 − + 𝜋 0 (𝐶 𝑃 𝑅𝐻𝑆 =−1) ( 𝜏 2 =5.11× 10 −8 𝑠

Introduction dn ~ θs .(6×10-17) e.cm dn < 3 × 10-26 e.cm Why EDM is Interesting? CP-violation: Natural kaon decay cont.. CP violation shows that weak interactions don’t treat the matter the same as anti-matter and this would leave the abundance of matter over anti-matter. Source of CP violation comes from the SM-CKM matrix in the form of δCP . Strong CP problem Ref. J M Pendlebury et al. Phys. Rev. D 92.9 (Nov. 2015) Maxim Pospelov and Adam Ritz. Ann. Phys. 318.1 (July 2005), dn ~ θs .(6×10-17) e.cm dn < 3 × 10-26 e.cm θs  < 5 × 10-10 The Smallness of the value of θs is unknown, also known as CP problem. CPT (and Lorentz) Symmetry Quantum field theory is invariant under CPT transformation –recover the original vector after successive C, P, T transforms. Any deviation from CPT invariance is beyond the SM and will involve new physics. Hence precision test of CPT invariance is a powerful way to gain insights into aspects of possible new physics.

Introduction Why EDM is Interesting? Baryon Asymmetry of the Universe (BAU) BAU is quantified as the a ratio between the density of surviving matter (nB) to photons (nγ). Precisely measured value of  ηB in cosmic microwave background observation reported by planks telescope is [Ref. Canetti et al.] BAU computed using the known source of CP violation in CKM-matrix [Ref. Riotto et al.]: BAU calculated using known source of CP violation is too small and there should be additional new source of CP-violations and corresponding new physics Beyond the Standard Model (BSM). Laurent Canetti, Marco Drewes, and Mikhail Shaposhnikov. “Matter and antimatter in the universe”. en. In: New J. Phys.14.9 (Sept. 2012 Antonio Riotto and Mark Trodden. “Recent progress in Baryogenesis”. In: Annu. Rev. Nucl. Part. Sci. 49.1 (Dec. 1999)

Introduction 𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏 Why EDM is Interesting? EDM and CP-Violation A. Yoshimi RIEKN (https://slideplayer.com/slide/8243393/) 𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏 T EDM Spin _ + P Zheng-Tian Lu et al.

Attempts to Measure the EDM EDM may generate from one or many CP violating mechanism. Non-zero EDM is elementary particles, subatomic composite particles , nuclei and atoms in their ground state indicates CPV. Only non-degenerate states possessing non-zero EDM violates CP Non-zero EDM of molecule does not necessarily indicate the CPV. Attempts over the last five decades at measuring a CPV EDM in many systems have resulted in stringent upper limit. Ref. Jungmann et. al., 2017 (https://journals.jps.jp/doi/10.7566/JPSCP.18.011017)

Attempts to Measure the EDM Attempts over the last five decades at measuring a CPV EDM in many systems have resulted in stringent upper limit. Ref. Jungmann et. al., 2017.

General Technique Ramsey Method:

General Technique Ramsey Method: Begins with polarized ensemble, magnetization is aligned in z axis same as magnetic field RF-oscillating field is applied in xy direction Figure illustrating the steps involved in the Ramsey method. An initial state with magnetization: Courtesy: P. Schmidt-Wellenburg (2016).

Measured and Theoretical EDM Value 10-23 10-26 10-29 10-32 10-32 10-38 10-44 Fig: panel showing the measured and theoretical value of EDM for leptons and baryons. The measured upper limit of EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. [Ref. P. Mohanmurthy]

Measured and Theoretical EDM Value 10-22 10-26 10-32 The measured upper limit of atomic EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. [Ref. P. Mohanmurthy]

Need of Octupole-Deformed Nuclei Octupole deformed nuclei and EDM EDM searches in different systems are complementary since they are sensitive to different linear combination of CP-violation sources. Paramagnetic molecules and atoms: Tl, YbF, ThO, HfF+ have single unpaired electrons and are sensitive to an intrinsic electron EDM. The contribution of electron EDM in paramagnetic system is amplified by the relativistic atomic structure of the heavy alkali-like atoms and are sensitive to nuclear spin independent CP-violating electron-nucleon interactions. The diamagnetic atoms and molecules:   199Hg, 129Xe, 225Ra, TIF have a appearance of partially screened nucleus and are sensitive to isoscalar and isovector CP-violating interaction inside the nucleus. Diamagnetic atoms have relatively very small contributions from individual electron, proton or neutron EDM, compared to contributions from nuclear Schiff moment. According to Schiff theorem, nuclear EDM in diamagnetic systems is almost completely screened by the surrounding electron cloud. This screening is not perfect for the heavy nuclei due to relativistic atomic structure, and contribute residual effect to the atomic EDM also called Schiff moment. [Ref. Jaideep Singh 2019, https://arxiv.org/abs/1903.03206]

Need of Octupole-Deformed Nuclei Octupole deformed nuclei and EDM Nuclei EDM enhancement w.r.t 99Hg 221,223Rn 102 225Ra 103 229Pa 105 Ref. Jaideep Singh 2019 199Hg currently sets the most stringent limits on CP-violating interactions originating from nuclear medium. Diamagnetic atoms such as 225Ra, 221,223Rn, 229Pa have a pear-shaped (octupole-deformed) nuclei. Octupole deformed characterized by β3 has nearly degenerate parity doublets. Due to the parity-violating nucleon-nucleon interaction, the two states that make up the parity doublet mix and result in an enhanced Schiff moment.

Need of Octupole-Deformed Nuclei Octupole deformation zone in Z, N isotope plot A = 270 N = 84 -88 Z = 54 -70 N = 130-136 Z = 84 -92 Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree-Fock plus BCS model @S. Ebata et al. (https://arxiv.org/pdf/1707.07416.pdf)

Need of Octupole-Deformed Nuclei Octupole deformed nuclei and EDM Contribution of atomic EDM due to Schiff moment: β2 - quadrupole deformation parameter β3 - octupole deformation parameter ∆E - energy different between the parity doublets Larmor frequency of spin-1/2 particles: For the uniform magnetic field, ∆B =0, and frequency difference is directly proportional to EDM. Hence, the uncertainty in EDM is solely given by the uncertainty in frequency measurement. The difference in two frequency is: Ref. Jaidep Singh et al., https://link.springer.com/article/10.1007/s10751-019-1573-z Spevak et. Al., Phys. Rev. C 56, 1357 Auerbach et. Al., Phys. Rev. Lett. 76, 4316 

Need of Octupole-Deformed Nuclei Octupole deformed nuclei and EDM Contribution of atomic EDM due to Schiff moment: β2 - quadrupole deformation parameter β3 - quadrupole deformation parameter ∆E - energy different between the parity doublets Which is ideally the inverse of spin precession time (τ): Nm = number of frequency different measurements Na  = total number of particles probed T = total integration time ε = experimental efficiency [Ref. Jaideep Singh 2019, https://arxiv.org/abs/1903.03206]

Need of Octupole-Deformed Nuclei Statistical Sensitivity to EDM measurement Sector Exp. Limit (e-cm) Method Standard Model Electron 1.1 x 10-29 ThO in a beam 10-44 Neutron 3 x 10-26 UCN in a bottle 10-32 199Hg 6.2 x 10-30 Hg atoms in a cell 10-35 Ref. M. Ramsey-Musolf (2009) No experimental evidence for a permanent EDM in any System

Need of Octupole-Deformed Nuclei Statistical Sensitivity to EDM measurement Nuclei shorting were based on: Nuclei with better octupole deformation than 225Ra. Nuclei with relative quiet branches of decay (not too noisy): i.e., long halftimes. Relatively well known magnetometry and atomic spectroscopy like Fr, Ra, Hg, Cs, TI, Y and so on. EDM enhance were calculated based on: a Theoretical Enhancement→(β2 β32 Z3 A2∕3)/ΔE bStatistical Sensitivity→ √(Beam rates × T1∕2) cBeam Sensitivity→ √(T1∕2) dComparison of Theoritical Sensitivity w.r.t Statistical Sensitivity →Theoretical Enhancement × Statistical Sensitivity

Survey Results

Results and Conclusions… Table-I: Potential Octupole Deformed Nuclei for EDM Measurement Results and Conclusions… S.N. Nuclei T1/2 β3 β2 𝑱 𝝅 𝜟E Th. enh. FRIB Yield (×106) Stat. Sens. Beam Sens. EDM enh. 1 221Rn86 25(2)min [Jain2007] 0.142 [ATNDT] 0.119 [ATNDT] 7/2+ [Jain2007] NoState -  2.29 0.02 0.60 - 2 223Rn86 24.3(4) min [Browne2001] 0.117 [ATNDT] 0.155 [ATNDT] 7/2 [Brwone2001]  - 0.9 0.01 0.37 3 225Rn86 4.66(4) min [Jain2008] 0.077 [ATNDT] 0.163 [ATNDT] 7/2- [Jain2008] 0.27 0.00 0.21 4 223Ra88 11.43(5)days [Browne2001] 0.156 [ATNDT] 3/2+ [Browne2001] 50.13(1) [Brwone2001] 1.36 6.08 0.85 0.97 1.33 5 225Ra88 14.9(2) days [Jain2009] 0.124 [ATNDT] 0.164 [ATNDT] 1/2+ [Jain2009] 55.16(6) [Jain2009] 1.00 6.41 6 225Ac89 9.9203(3) days [Jain2009] 0.127 [ATNDT] 3/2- [Jain2009] 40.1 [Spevak1996] 1.49 5.1 0.73 0.89 7 226Ac89 29.37(12) hours [Akovali1996] 0.12 [ATNDT] 1 [Akovali1996] 5.78 0.95 8 221Fr87 4.9(2) min [Jain2007] 0.1 [Apevak1996] 0.106 [Spevak1996] 5/2- [Jain2007] 234.51(5) [Jain2007] 0.09 6.13 0.98 9 223Fr87 22.00(7) min [Browne2001] 0.135 [ATNDT] 0.146 [ATNDT] 3/2- [Browne2001] 160.51(5) [Spevak1996] 0.35 4.26 0.03 0.82 0.28 10 225Fr87 3.95 (14)min [Jain2008] 0.108 [ATNDT] 2.08 0.57 11 227Fr87 2.47(3) min [ICTP2016] 0.07 [ATNDT] 0.181 [ATNDT] 1/2+ [ICTP2016] 62.97(7) [ICTP2016] 0.30 7.02 1.05 0.31 12 229Th90 7880(120) yr [Brwone2008] 0.24 [Minkov2017] 0.115 [Minkov2017] 5/2+ [Browne2008] 133.3 [Flambaum2019] 1.07 6.19 431.75 13 229Pa91 1.50(5) days [Browne2008] 0.082 [Spevak1996] 0.19 [ATNDT] 5/2+ [Brwone2008] 0.06(5) [Ahmad2015] 521.13 20.7 1.80 936.49

Results and Conclusions… Table-I: Potential Deformed Nuclei for EDM Measurement (cont..) Results and Conclusions… S.N. Nuclei T1/2 β3 β2 𝑱 𝝅 𝜟E Th. enh. FRIB Yield (×106) Stat. Sens. Beam Sens. EDM enh. 14 223Ac89 2.10(5)min [Jain2007] 0.0.151 [ATNDT] 0.147 [ATNDT] 5/2- [Browne2001] 50.7(1) [Browne2001] 1.49 8.18 0.01 0.9 15 227Ac89 21.772(3) year [ICTP2014]] 0.105 [ATNDT] 0.172 [ATNDT] 3/2- [Brwone2001] 27.369(11) [ICPT2014]  1.56 6.4 23.08 1.0 1.56 16 221Ra88 104(1) s [Jain2008] Not measured 0.207 [ATNDT] 5/2+ [Brwone2013] 95.50(9) [Browne2013] - 6.34 0.91 Numbers are normalized to 225Ra at FRIB

Results and Conclusions… Table-I: Octupole Deformed Nuclei for EDM Measurement S.N. Nuclei T1/2 β3 β2 𝑱 𝝅 𝜟E Th. enh. FRIB Yield (×106) Stat. Sens. Beam Sens. EDM enh. 1 221Rn86 25(2)min [Jain2007] 0.142 [ATNDT] 0.119 [ATNDT] 7/2+ [Jain2007] NoState -  2.29 0.02 0.60 - 2 223Rn86 24.3(4) min [Browne2001] 0.117 [ATNDT] 0.155 [ATNDT] 7/2 [Brwone2001]  - 0.9 0.01 0.37 3 225Rn86 4.66(4) min [Jain2008] 0.077 [ATNDT] 0.163 [ATNDT] 7/2- [Jain2008] 0.27 0.00 0.21 4 223Ra88 11.43(5)days [Browne2001] 0.156 [ATNDT] 3/2+ [Browne2001] 50.13(1) [Brwone2001] 1.36 6.08 0.85 0.97 1.33 5 225Ra88 14.9(2) days [Jain2009] 0.124 [ATNDT] 0.164 [ATNDT] 1/2+ [Jain2009] 55.16(6) [Jain2009] 1.00 6.41 6 225Ac89 9.9203(3) days [Jain2009] 0.127 [ATNDT] 3/2- [Jain2009] 40.1 [Spevak1996] 1.49 5.1 0.73 0.89 7 226Ac89 29.37(12) hours [Akovali1996] 0.12 [ATNDT] 1 [Akovali1996] 5.78 0.95 8 221Fr87 4.9(2) min [Jain2007] 0.1 [Apevak1996] 0.106 [Spevak1996] 5/2- [Jain2007] 234.51(5) [Jain2007] 0.09 6.13 0.98 9 223Fr87 22.00(7) min [Browne2001] 0.135 [ATNDT] 0.146 [ATNDT] 3/2- [Browne2001] 160.51(5) [Spevak1996] 0.35 4.26 0.03 0.82 0.28 10 225Fr87 3.95 (14)min [Jain2008] 0.108 [ATNDT] 2.08 0.57 11 227Fr87 2.47(3) min [ICTP2016] 0.07 [ATNDT] 0.181 [ATNDT] 1/2+ [ICTP2016] 62.97(7) [ICTP2016] 0.30 7.02 1.05 0.31 12 229Th90 7880(120) yr [Brwone2008] 0.24 [Minkov2017] 0.115 [Minkov2017] 5/2+ [Browne2008] 133.3 [Flambaum2019] 1.07 6.19 431.75 13 229Pa91 1.50(5) days [Browne2008] 0.082 [Spevak1996] 0.19 [ATNDT] 5/2+ [Brwone2008] 0.06(5) [Ahmad2015] 521.13 20.7 1.80 936.49 Results and Conclusions…

Results and Conclusions… Table-I: Octupole Deformed Nuclei for EDM Measurement (cont..) Results and Conclusions… S.N. Nuclei T1/2 β3 β2 𝑱 𝝅 𝜟E Th. enh FRIB Yield (×106) Stat. Sens. Beam Sens. DM enh. 14 223Ac89 2.10(5)min [Jain2007] 0.0.151 [ATNDT] 0.147 [ATNDT] 5/2- [Browne2001] 50.7(1) [Browne2001] 1.49 8.18 0.01 0.9 15 227Ac89 21.772(3) year [ICTP2014]] 0.105 [ATNDT] 0.172 [ATNDT] 3/2- [Brwone2001] 27.369(11) [ICPT2014]  1.56 6.4 23.08 1.0 1.56 16 221Ra88 104(1) s [Jain2008] Not measured 0.207 [ATNDT] 5/2+ [Brwone2013] 95.50(9) [Browne2013] - 6.34 0.91 Numbers are normalized to 225Ra at FRIB

Table-II: Additional Nuclei with Suspected Octupole Deformation (No calculation performed yet) S.N Nuclei T1/2 β3 pred. β2 pred. 𝑱 𝝅 𝜟E Th. Sens FRIB Yield (×106) Stat. Sens. Beam Sens. EDM enhancement 1 187Au79 8.3(2) min [Basunia2009] ? 0.156 [ATNDT] 1/2+ [Basunia2009] 274.91(16) [Basaunia2009] -  33.8 0.05 2.30 - 2 189Au79 28.7(4) min [Johnson2017] 0.148 [ATNDT] 1/2+ [Johnson2017] 814.30(25) [Johnson2017]  - 58.6 0.11 3.02 3 231Ac89 7.5(7) min [Brwone2013] 0.207 [ATNDT] 1/2+ [Browne2013] 372.28(8) [Browne2013] 52.7 2.87 4 233Ac89 2.4(2) min [Singh2005] 0.215 [ATNDT] 1/2+ [Singh2005] 1/2- state not measured 26.7 0.02 2.04 5 235Th90 7.2(7) min [Browne2014] 0.215 [ATNDT]] 1/2+ [Brwone2014] 6.72 1.02 6 233Th90 21.83(4) min [Singh2005] 539.61(2) [Singh2005] 6.43 0.03 1.00 7 237Pa91 8.7(2) min [Basunia2006] 1/2+ [Basunia2006] 6.91 1.04 8 239Pu94 24110(30) year [Brwone20014] 0.223 [ATNDT] Not measured Data Not available 9 241Cm96 32.8(2) days [Nesaraja2005] 1/2+ [Nesaraja2005] Octupole deformations come in clusters. These species here are inside the region, but haven't been calculated as most previous calculations used some simplified system like even-even systems (Ref. Sylvester et. al.,)

Table-III: Additional Octupole Deformed Nuclei (might be useful for different EDM measurement techniques) S.N Nuclei T1/2 β3 pred. β2 pred. 𝑱 𝝅 𝜟E Th. Sens FRIB Yield (×106) Stat. Sens. Beam Sens. EDM enhancement 1 220Ra88 18(2)ms 0.144 [ATNDT] 0.103 [ATNDT]  0+ - 0.8 2 224Ra88 3.6319(23)days [Singh2015] 0.131 [ATNDT] 0.164 [ATNDT] 0+ [Singh2015] 6.8 3 226Ra88 1600(7) Year [Akovali1996] 0.108 [ATNDT] 0.172 [ATNDT] 0+ [Akovali1996] 5.61 4 224Ac89 2.78(16) hour 0.165 [ATNDT] 0- 4.45

Results and Conclusions…

Results and Conclusion We have performed the global survey of potential octupole deformed candidate atomic nuclei for the EDM enhancement Figure out 7 viable nuclei for the future measurement at FRIB facility which are equally or more sensitive than 225Ra. Nuclei EDM Sensitivity compared to 225Ra 223Ra88 1.33 225Ra88 1.00 223Ac89 1.34 225Ac89 227Ac89 1.56 229Th90 1.05 229Pa91 936.49 Numbers are normalized to 225Ra at FRIB

Future Research We have requested the Dr. Anatoli’s group @Msstate for the theoretical calculation of β3 value of some of our suspected octupole-deformed nuclei. Will be writing the proposal at FRIB for measuring the EDM value of some of the most EDM sensitive nuclei.

List of selected references 1 [Singh2011] S. Singh et al. Nucl Data Sheet 111, 2851 (2011) 3 [ATNDT] P. Moller et al., Atomic Data & Nuclear Data Table, 59, 485-38 (1995) 2 [FRIB] https://groups.nscl.msu.edu/frib/rates/fribrates.html 4 [Browne2001] E. Browne, Nucl Data Sheet 93, 843 (2001) 5 [Jain2009] A. K. Jain et al. Nucl Data Sheet 110, 1409 (2009) 6 [Akovali1996] Y. A. Akovali Nucl Data Sheet 77, 443 (1996) 7 [ICTP2016] Ictp-2014 Worskhoop Group, Nucl Data Sheet 132, 257 (2016) 8 [Brwone2008] E. Brwone et al., Nucl Data Sheet 109, 2657 (2008) 9 [Basunia2009] M. S. Basunia Nucl Data Sheet 110, 999 (2009) 10 [Johnson2017] T. D. Johnson et al., Nucl Dtat Sheet 142, 1(2017) 11 [Browne2013] E. Browne et al., Nucl Data Sheet 114, 751, 2013 12 [Singh2005] B. Singh et al., Nucl Data Sheet105, 109 (2005) 13 [Brwone2014] E. Brwone et al., Nucl Data Sheet 122, 205 (2014) 14 [Basunia2006] M. S. Basunia Nucl Data Sheet 107, 2323 (2006) 15 [Nesaraja2005] C. D. Nesaraja , Nucl Data Sheet 130, 183(2005) 16 [Singh2015] S. Singh et al. Nucl Data Sheet 130, 127 (2015) 17 E. Browne et al., NDS 109, 2657 (2008) 18 [Minkov2017] N. Minkov et al., Phys. Rev. Lett 118 212501 (2017) 19 Y. A. Akovali NDS 77, 433 (1996) 20 E. Browne et al., NDS 93, 846 (2001) 21 [Jain2008] A. K. Jain et al., NDS 110, 1409 (2009) 22 [Jain2007] A. K. Jain et al., NDS 108, 883 (2007) 23 [SIngh2006] B. Singh, NDS 108, 79 (2007) 24 [Timar2014] J. Timar et al., NDS 121, 143, (2014) 25 [Ahmad2015] I Ahmad et al., Phys. Rev. C 92, 024313 (2015) 26 [Spevak1996] V. Spevak et al., Phys. Rev. C 56,3 (1997) 27 [Lender1988] G. A. Lender et al., Phys. Rev. C 37 (1988) 28 [Flambaum2019] V. V. Flambaum, Phys. Rev. C 99, 035501 (2019)

MENU-2019 Thank You! My major advisor Dr. Jeff A. Winger. Acknowledgement My major advisor Dr. Jeff A. Winger. Co-authors of this work: Mr. P. Mohanmurthy and Mr. D. P. Siwakoti Office of Science, Department of Energy for supporting through travel fund. Thank You! MENU-2019 October 25-28, 2017 Pittsburgh, PA Cohen University Center, CMU June 02-07 Pittsburgh, PA

General Technique Ramsey Method: Fig. comparison between Rabi and Ramsey method. Ramsey oscillation is much narrow Statistical Sensitivity in Ramsey method is:

Measured and Theoretical EDM Value The measured upper limit of molecular EDM at 90% C.L. has been shown in red. The gray portion represents the contributions of QCD-θs, where as the purple color shows the contribution from SM-CKM matrix. Ref. P. Mohanmurthy.

𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏 Ongoing Effort for EDM Measurement 𝒅≠𝟎⇒𝑻−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏⇒𝑪𝑷−𝑽𝒊𝒐𝒍𝒂𝒕𝒊𝒐𝒏

Results and Conclusions… EDM of 225Ra enhanced and more reliably calculated Results and Conclusions… Closely spaced parity doublet – Haxton & Henley, PRL (1983) Large Schiff moment due to octupole deformation – Auerbach, Flambaum & Spevak, PRL (1996) Relativistic atomic structure (225Ra / 199Hg ~ 3) – Dzuba, Flambaum, Ginges, Kozlov, PRA (2002) - = (|a - |b)/2 + = (|a + |b)/2 55 keV |a |b Parity doublet Enhancement Factor: EDM (225Ra) / EDM (199Hg) Isoscalar Isovector Skyrme SIII 300 4000 Skyrme SkM* 2000 Skyrme SLy4 700 8000 Schiff moment of 225Ra, Dobaczewski, Engel, PRL (2005) Schiff moment of 199Hg, Dobaczewski, Engel et al., PRC (2010) “[Nuclear structure] calculations in Ra are almost certainly more reliable than those in Hg.” – Engel, Ramsey-Musolf, van Kolck, Prog. Part. Nucl. Phys. (2013) Constraining parameters in a global EDM analysis. – Chupp, Ramsey-Musolf, arXiv1407.1064 (2014)

Results and Conclusions… Nuclei shorting based on: Find nuclei with better octupole deformation than 225Ra Species is at least long lived as 225Ra With relative quiet branches of decay (not too noisy) Relatively well known magnetometry and atomic spectroscopy like Fr, Ra, HG, Cs, TI, Y and so on. No experimental evidence for a permanent EDM in any System 𝑑 𝑒 <1.6× 10 −27 𝑒.𝑐𝑚 𝑑 𝐻𝑔 <2.1× 10 −28 𝑒.𝑐𝑚 𝑑 𝑛 <6.3× 10 −20 𝑒.𝑐𝑚 B.C. Regan et al., Phys. Rev. Lett. 88, 071805 (2002) (90% C.L.) M.V Romalis et al., Phys. Rev. Lett. 86, 2505 (2001) (90% C.L.) P.G. Harris et al., Phys. Rev. Lett. 82, 904 (1999) (90% C.L.)

Results and Conclusions… J. Engel @https://www.physics.umass.edu/acfi/sites/acfi/files/slides/dipole-amherst.pdf